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在学习代数学之余，值得一看的代数学书籍。里面介绍了更为丰富的代数学概念和结论。PREFACEMy purpose in this book is to treat linear transformations on finite-dimensional vector spaces by the methods of more general theories. Theidea is to emphasize the simple geometric notions common to many partsof mathematics and its applications, and to do so in a language that givesaway the trade secrets and tells the student what is in the back of the mindsof people proving theorems about integral equations and Hilbert spaces.The reader does not, however, have to share my prejudiced motivationExcept for an occasional reference to undergraduate mathematics the bookis self-contained and may be read by anyone who is trying to get a feelingfor the linear problems usually discussed in courses on matrix theory orhigher"algebra. The algebraic, coordinate-free methods do not lose powerand elegance by specialization to a finite number of dimensions, and theyare, in my belief, as elementary as the classical coordinatized treatmentI originally intended this book to contain a theorem if and only if aninfinite-dimensional generalization of it already exists, The temptingeasiness of some essentially finite-dimensional notions and results washowever, irresistible, and in the final result my initial intentions are justbarely visible. They are most clearly seen in the emphasis, throughout, ongeneralizable methods instead of sharpest possible results. The reader maysometimes see some obvious way of shortening the proofs i give In suchcases the chances are that the infinite-dimensional analogue of the shorterproof is either much longer or else non-existent.A preliminary edition of the book (Annals of Mathematics Studies,Number 7, first published by the Princeton University Press in 1942)hasbeen circulating for several years. In addition to some minor changes instyle and in order, the difference between the preceding version and thisone is that the latter contains the following new material:(1) a brief dis-cussion of fields, and, in the treatment of vector spaces with inner productsspecial attention to the real case.(2)a definition of determinants ininvariant terms, via the theory of multilinear forms. 3 ExercisesThe exercises(well over three hundred of them) constitute the mostsignificant addition; I hope that they will be found useful by both studentPREFACEand teacher. There are two things about them the reader should knowFirst, if an exercise is neither imperative "prove that.., )nor interrogtive("is it true that...?" )but merely declarative, then it is intendedas a challenge. For such exercises the reader is asked to discover if theassertion is true or false, prove it if true and construct a counterexample iffalse, and, most important of all, discuss such alterations of hypothesis andconclusion as will make the true ones false and the false ones true. Secondthe exercises, whatever their grammatical form, are not always placed 8oas to make their very position a hint to their solution. Frequently exer-cises are stated as soon as the statement makes sense, quite a bit beforemachinery for a quick solution has been developed. A reader who tries(even unsuccessfully) to solve such a"misplaced"exercise is likely to ap-preciate and to understand the subsequent developments much better forhis attempt. Having in mind possible future editions of the book, I askthe reader to let me know about errors in the exercises, and to suggest im-provements and additions. (Needless to say, the same goes for the text.)None of the theorems and only very few of the exercises are my discovery;most of them are known to most working mathematicians, and have beenknown for a long time. Although i do not give a detailed list of my sources,I am nevertheless deeply aware of my indebtedness to the books and papersfrom which I learned and to the friends and strangers who, before andafter the publication of the first version, gave me much valuable encourage-ment and criticism. Iam particularly grateful to three men: J. L. Dooband arlen Brown, who read the entire manuscript of the first and thesecond version, respectively, and made many useful suggestions, andJohn von Neumann, who was one of the originators of the modern spiritand methods that I have tried to present and whose teaching was theinspiration for this bookP、R.HCONTENTS的 FAPTERPAGRI SPACESI. Fields, 1; 2. Vector spaces, 3; 3. Examples, 4;4. Comments, 55. Linear dependence, 7; 6. Linear combinations. 9: 7. Bases, 108. Dimension, 13; 9. Isomorphism, 14; 10. Subspaces, 16; 11. Calculus of subspaces, 17; 12. Dimension of a subspace, 18; 13. Dualspaces, 20; 14. Brackets, 21; 15. Dual bases, 23; 16. Reflexivity, 24;17. Annihilators, 26; 18. Direct sums, 28: 19. Dimension of a directsum, 30; 20. Dual of a direct sum, 31; 21. Qguotient spaces, 33;22. Dimension of a quotient space, 34; 23. Bilinear forms, 3524. Tensor products, 38; 25. Product bases, 40 26. Permutations41; 27. Cycles,44; 28. Parity, 46; 29. Multilinear forms, 4830. Alternating formB, 50; 31. Alternating forms of maximal degree,52II. TRANSFORMATIONS32. Linear transformations, 55; 33. Transformations as vectors, 5634. Products, 58; 35. Polynomials, 59 36. Inverses, 61; 37. Mat-rices, 64; 38. Matrices of transformations, 67; 39. Invariance,7l;40. Reducibility, 72 41. Projections, 73 42. Combinations of pro-jections, 74; 43. Projections and invariance, 76; 44. Adjoints, 78;45. Adjoints of projections, 80; 46. Change of basis, 82 47. Similarity, 84; 48. Quotient transformations, 87; 49. Range and null-space, 88; 50. Rank and nullity, 90; 51. Transformations of rankone, 92 52. Tensor products of transformations, 95; 53. Determinants, 98 54. Proper values, 102; 55. Multiplicity, 104; 56. Triangular form, 106; 57. Nilpotence, 109; 58. Jordan form. 112III ORTHOGONALITY11859. Inner products, 118; 60. Complex inner products, 120; 61. Innerproduct spaces, 121; 62 Orthogonality, 122; 63. Completeness, 124;64. Schwarz e inequality, 125; 65. Complete orthonormal sets, 127;CONTENTS66. Projection theorem, 129; 67. Linear functionals, 130; 68. P aren, gBCHAPTERtheses versus brackets, 13169. Natural isomorphisms, 138;70. Self-adjoint transformations, 135: 71. Polarization, 13872. Positive transformations, 139; 73. Isometries, 142; 74. Changeof orthonormal basis, 144; 75. Perpendicular projections, 14676. Combinations of perpendicular projections, 148; 77. Com-plexification, 150; 78. Characterization of spectra, 158; 79. Spec-ptral theorem, 155; 80. normal transformations, 159; 81. Orthogonaltransformations, 162; 82. Functions of transformations, 16583. Polar decomposition, 169; 84. Commutativity, 171; 85. Self-adjoint transformations of rank one, 172IV. ANALYSIS....17586. Convergence of vectors, 175; 87. Norm, 176; 88. Expressions forthe norm, 178; 89. bounds of a self-adjoint transformation, 17990. Minimax principle, 181; 91. Convergence of linear transformations, 182 92. Ergodic theorem, 184 98. Power series, 186APPENDIX. HILBERT SPACERECOMMENDED READING, 195INDEX OF TERMS, 197INDEX OF SYMBOLS, 200CHAPTER ISPACES§L. FieldsIn what follows we shall have occasion to use various classes of numbers(such as the class of all real numbers or the class of all complex numbers)Because we should not at this early stage commit ourselves to any specificclass, we shall adopt the dodge of referring to numbers as scalars. Thereader will not lose anything essential if he consistently interprets scalarsas real numbers or as complex numbers in the examples that we shallstudy both classes will occur. To be specific(and also in order to operateat the proper level of generality) we proceed to list all the general factsabout scalars that we shall need to assume(A)To every pair, a and B, of scalars there corresponds a scalar a+called the sum of a and B, in such a way that(1) addition is commutative,a+β=β+a,(2)addition is associative, a+(8+y)=(a+B)+y(3 there exists a unique scalar o(called zero)such that a+0= a forevery scalar a, and(4)to every scalar a there corresponds a unique scalar -a such that十(0(B)To every pair, a and B, of scalars there corresponds a scalar aBcalled the product of a and B, in such a way that(1)multiplication is commutative, aB pa(2)multiplication is associative, a(Br)=(aB)Y,( )there exists a unique non-zero scalar 1 (called one)such that al afor every scalar a, and(4)to every non-zero scalar a there corresponds a unique scalar a-1or-such that aaSPACES(C)Multiplication is distributive with respect to addition, a(a+n)If addition and multiplication are defined within some set of objectsscalars) so that the conditions(A),B), and (c)are satisfied, then thatset(together with the given operations) is called a field. Thus, for examplethe set Q of all rational numbers(with the ordinary definitions of sumand product)is a field, and the same is true of the set of all real numberaand the set e of all complex numbersHHXERCISIS1. Almost all the laws of elementary arithmetic are consequences of the axiomsdefining a field. Prove, in particular, that if 5 is field and if a, and y belongto 5. then the following relations hold80+a=ab )Ifa+B=a+r, then p=yca+(B-a)=B (Here B-a=B+(a)(d)a0=0 c=0.(For clarity or emphasis we sometimes use the dot to indi-cate multiplication.()(-a)(-p)(g).If aB=0, then either a=0 or B=0(or both).2.(a)Is the set of all positive integers a field? (In familiar systems, such as theintegers, we shall almost always use the ordinary operations of addition and multi-lication. On the rare occasions when we depart from this convention, we shallgive ample warningAs for "positive, "by that word we mean, here and elsewherein this book, "greater than or equal to zero If 0 is to be excluded, we shall say"strictly positive(b)What about the set of all integers?(c) Can the answers to these questiong be changed by re-defining addition ormultiplication (or both)?3. Let m be an integer, m2 2, and let Zm be the set of all positive integers lessthan m, zm=10, 1, .. m-1). If a and B are in Zmy let a +p be the leastpositive remainder obtained by dividing the(ordinary) sum of a and B by m, andproduct of a and B by m.(Example: if m= 12, then 3+11=2 and 3. 11=9)a) Prove that i is a field if and only if m is a prime.(b What is -1 in Z5?(c) What is囊izr?4. The example of Z, (where p is a prime)shows that not quite all the laws ofelementary arithmetic hold in fields; in Z2, for instance, 1 +1 =0. Prove thatif is a field, then either the result of repeatedly adding 1 to itself is always dif-ferent from 0, or else the first time that it is equal to0 occurs when the numberof summands is a prime. (The characteristic of the field s is defined to be 0 in thefirst case and the crucial prime in the second)SEC. 2VECTOR SPACES35. Let Q(v2)be the set of all real numbers of the form a+Bv2, wherea and B are rational.(a)Ie(√2) a field?(b )What if a and B are required to be integer?6.(a)Does the set of all polynomials with integer coefficients form a feld?(b)What if the coeficients are allowed to be real numbers?7: Let g be the set of all(ordered) pairs(a, b)of real numbers(a) If addition and multiplication are defined by(a月)+(,6)=(a+y,B+6)and(a,B)(Y,8)=(ary,B6),does s become a field?(b )If addition and multiplication are defined by(α,月)+⑦,b)=(a+%,B+6)daB)(,b)=(ay-6a6+的y),is g a field then?(c)What happens (in both the preceding cases)if we consider ordered pairs ofcomplex numbers instead?§2. Vector spaceWe come now to the basic concept of this book. For the definitionthat follows we assume that we are given a particular field s; the scalarsto be used are to be elements of gDEFINITION. A vector space is a set o of elements called vectors satisfyingthe following axiomsQ (A)To every pair, a and g, of vectors in u there corresponds vectora t y, called the aum of a and y, in such a way that(1)& ddition is commutative,x十y=y十a(2)addition is associative, t+(y+2)=(+y)+a(3)there exists in V a unique vector 0(called the origin) such thata t0=s for every vector and(4)to every vector r in U there corresponds a unique vector -rthat c+(-x)=o(B)To every pair, a and E, where a is a scalar and a is a vector in u,there corresponds a vector at in 0, called the product of a and a, in sucha way that(1)multiplication by scalars is associative, a(Bx)=aB)=, and(2 lz a s for every vector xSPACESSFC B(C)(1)Multiplication by scalars is distributive with respect to vectorddition, a(+y=a+ ag, and2)multiplication by vectors is distributive with respect to scalar ad-dition, (a B )r s ac+ Bc.These axioms are not claimed to be logically independent; they aremerely a convenient characterization of the objects we wish to study. Therelation between a vector space V and the underlying field s is usuallydescribed by saying that v is a vector space over 5. If S is the field Rof real number, u is called a real vector space; similarly if s is Q or if gise, we speak of rational vector spaces or complex vector space§3. ExamplesBefore discussing the implications of the axioms, we give some examplesWe shall refer to these examples over and over again, and we shall use thenotation established here throughout the rest of our work.(1) Let e(= e)be the set of all complex numbers; if we interpretr+y and az as ordinary complex numerical addition and multiplicatione becomes a complex vector space2)Let o be the set of all polynomials, with complex coeficients, in avariable t. To make into a complex vector space, we interpret vectoraddition and scalar multiplication as the ordinary addition of two poly-nomials and the multiplication of a polynomial by a complex numberthe origin in o is the polynomial identically zeroExample(1)is too simple and example (2)is too complicated to betypical of the main contents of this book. We give now another exampleof complex vector spaces which(as we shall see later)is general enough forall our purposes.3)Let en,n= 1, 2,. be the set of all n-tuples of complex numbers.Ix=(1,…,轨)andy=(m1,…,n) are elements of e, we write,,bdefinitionz+y=〔1+叽,…十物m)0=(0,…,0),-inIt is easy to verify that all parts of our axioms(a),(B), and (C),52, aresatisfied, so that en is a complex vector space; it will be called n-dimenaionalcomplex coordinate space

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XMP加密图片的提取工具。用它可以把游戏中加密的XMP图片提取出来保存为PNG图片。

优秀的贝叶斯统计学入门教材，简单明了，包含贝叶斯统计学的思想精华，值得一看高等院校统叶学写业规划教材贝叶斯统计峁诗松編著中团先计齿坂社京)新登字041号图书在版编目(CP数据贝叶斯统计/茆诗松编著一北京:中国统计出版衬,1999.9高等院校统计学规划教材ISN75037-29309.茆QI.贝叶斯统计-高等学校-教材IV.0212中国版本图惊CIP数据核字(1999第10216号作者虾诗松贲狂编辑/军责任校对:刘开颜封面设计:张建民出版发行中国统计版社通信地址/北京市二里河月坛街7号邮政编码09826办公地址/北点市丰台区哐三坏南路甲6号电话09)63459084、6326660(发行部印刷科伦克三莱印务(北京)有限公司经钠/新华书店斤本850×116mm132子数6千子印张{8.6印数/1-5)(册版别/上9910月第1版版次19作10月第1次印刷节号/SRN7-5037-2939.34定价15.6元中国统汁版图书,版权所有,侵权必究中国统计版图书,如有印装错误,本社发行部负责调换出版诜明“九五”期闾是我国社会主义市场经濟体制逐步完著和发展重要时期,一方面,随着髙等教育体制改革和统计改革的深入发展,对统计教育模式和统计人才培养目标都提出新的要求,另一方面科学技术的飞速发展也促使统计技术发生了重大交革,新理论、新方法畑新技穴不断涌现并被应用于统计实践活应这新形勢的需要,全国统计教树编审委员会制定了《1996-200年国统计教树建设规划》,根据《规划》的要求,编委会采取招标的方式组织全国有关院校的专家、学者编写了这批统计学专业“规教材”。这批教材力求以邓小理论为指早,在总结“八五”蝴间规捌统计教材建设经验的基础上,认真贯彻以下原则:①理论紧密联系实际的原则;巴解放思想、转变观念、大脰探索、努亦创新的原则;正确处理继承与发展关系的原则。通过不懈努力,把这批教材建设成为质量高,迺应性預、面向21世纪的新教材扫信通过这批教材的出版、发行;对推动我国统计教育改革和加快更新、改造我国统计教材体系、教村内容的岁伐将起到积极的促进作用,同时对我国统计教材建设也将起到較好的示范、导向作用。限于水平和经验这批教材的编宇、出版工作还会有缺点和不足处,诚恳欢迎教杖的使用单位、广大教师和同学们提出批评和建议全国統计教材編审委员会999年3月本书是按照全囯统计斆材编审委员会指定的《頃叶斯统计》編与大纲鳊写的,是供全倒商等学校玩计专业大学生知研究生学的教科与。贝叶斯统计在近50年中发展很快,内睿愈来食丰窨。这盟只选用其中最基不鄙分构成本书,相当一学期的肉容,本节力图疴学汀过传统的概率统计(颎率学派)课程的学生展示贝汁斯汽计的基本面貌,也使他们能了解员叶斯统计的基本思想,掌握叶疬统计的基本方法,为在实际中使用和研究贝叶斯统计打下了苠好的基础木书共六章,可分二部分。前三章国绕先验分布介绍贝叶所推断方法。后三章绕损失函数介绍贝叶斯决策方法。阅读这些内容仅需要攪率统计基本知识就部了。本书力剂利生劢衣趣的例于来说明贝"斯统计的基本想想和基本方法,尽量使读老对贝叶药统计产生兴趣,引发读者使用以叶斯方法去认识和解洪实际问题的望。进而云丰瘩和发展队叶蜥统计。假如学生的兴趣被钧出来,愿望被引出来,那么讲授这一门课的目的也基本达到贝叶斯统计是在与经典统计的争论中逐渐发展起来的。争论的闩题有:末知參数是酉可以看作随机变量?事件的慨率是否一定要有频率解释?概率是否可用经验兴确定?在这些河题的争论中贝叶斯学派建立起自已的理论与,在全球传播三有百年史的经與统计对统讦学的发展稗应屎起了巨大佐用,钽时乜暴露了一些问题。在小祥本问研究二、在区估计的解释}、在似然原理釣认识上等问题经典统计也受到只圬斯学派的评,在这出批评中贝叶斯学派也在不断完善叶斯计计决策论斯分析》一书在1980年和1985年熠继二畈问世把贝叶斯统计作了较完塾的叙述。在近20中只吐浙统计在实际中叉获得广泛的应用,I991年和I995年在美国连续岀版了二本《 Case studies in Bayesian Statistics》。使贝叶斯纨十在理论上刘实际上以及它们的结合上都得到了长足的发展。惧怕使用贝叶斯统计思想得到克服。如今贝汁斯统计也定进教室,打破经典统计独占教室的一统天下的局面,这不能不说是贝吽斯统计发展中的一些重要标志。贝叶斯统计已成为统计学中一个不可缺少的部分,相陀之下,贝叶斯统计在我国射应用与发展岢属起步阶長,但我厨有很好的发展叶斯统计的氛围。只要大家努力,如汁斯统计在我国一定能迅速发展,跟上世界主流。本书编写卣始至终得到国冢统计局教育中心的关心和帮助,有他们的督促,本书还会延期出版。上海财经大学张尧庭教授和中国人民大学的吴喜之教授耐心细致地审阅了全书,提出许多贵意见,笔者都认真考虑,并作修改.这使仝书增色不少。另外,何基报、硬娟、孙汊杰等阅读书稿,提出宇贵意见,还帮助打印会书,在此一并表丞感谢由于繃者水平有限,淮确表达只叶斯学派的各种观点并非易辜、错谬之处在所难凭,恳请国内同行和广大读若批评指正茆许松1999年1月30日2第·章先验分布与后验分布种信息总体信息样本信贝叶斯公式信息贝叶斯公式的密度函数形式共细女辱粉分在是三种信息的综合、共轭先验分布、后验分布的计算、共轭先验分布的优缺点四、常用的共轭先验分布超参数及其确定一、利用先验矩、利用完验分位数、利用验矩和先验分位数四、其它方法多参数模型充分统计量习题第二章贝叶斯推断条件方法佔计贝叶斯估计、贝叶斯估计的误差区间估计可信区间最大后验密度可信区间假设检验假设检验、贝叶斯因子三、简单假设对简单假设Q⊙四、复杂假设e对复杂假设回五、简单原假设对复杂的备择假设预测似然原理第三章先验分布的确定主观概率主观概率确定主观概率的方法利用先验信息确定先验分布、直方图法二、选定先验密度函数形式再估计其超参教三、定分度法与变分度法利用边缘分布确定先验密度、边缘分布二、混合分布、先验选择的四、先验选择的矩方法无信息先验分布贝叶斯假设一、位置参数的无信息先验尺度参数的无信息先验信息阵确定无信息先验多层先验多层先验、多层模型习题第四章泆策中的收益、损失与效用决策问趣的三妻素决策问题决策问题的三素决策准贝行动的容许性决策准则先验期望准则先验期望准则、两个性质损失函数从收益到损失、损大凶数损大凶数下的悲观准则四、损失凶数下的先验期望准则常用损失函数效用函数效用和效用函数效用的测定效用尺度四、常见的效用曲线五、用效用函数作决策的例子六、从效用到损失第五章贝叶斯决策贝叶斯决策问题后验风险准则验风殓决策函数后验风险准则常用损失数下的贝叶斯估计方损失函数下的贝叶斯估计二、线性损失函数下的贝叶斯估计限个行动问趣的假设检验抽样信息期望值完全信息期望值抽样信息期望值最佳样本量的确定抽样净益最佳样本量及其上界最佳样本量的求二行动线性决簧问题的正态分布下二行动线性决策问题的先验仄塔分布下二行动线性决策问题的先验、伽冯分布下二行动线性决策问题的先验习题第六章统计决策理论风险函数风险函数决策函数的最优性、统计决策中的点估计问题四、统计决策中的区间估计问题五、统计决策中的假没检验问题容许性、决策函数的容许性最小最大准则、最小最大准则最小最大估计的容许性贝叶斯风险贝叶斯风险贝叶期风险准则与后验风险准则的等价性贝叶期估计的性质俯录常用概率分布表附录标准正态分布函数Φ7表参考文献附录页录第一章先验分布与后验分布(1§1.]二种片息总体信息样本信2)、无验信息……公】.2贝叶斯公式………、贝叶斯公式的密度燃数形式(6)厅验分布是三种倍息的综合(8〕共轭先验分布…………〔13轭先验介布13、后验分布的计算甲血1■■日血血■D■三、共轭先验分布的优缺点、常用的共轲先验分布由■冒血…(19超郄数及其确定……利用光验矩、利用先验分位数三、利用先验矩和先验分位数…………阿、其它方法多参数模型1.6充分统计t……甲看省看甲『看■p甲P看■2031第二章贝叶斯推断2.1条件方法§2.2秸计36贝时斯估计

基本蛙跳程序 matlab/C混合蛙跳算法(SFLA)是一种基于群智能的亚启发式进化算法，并应用于离散组合优化问题的求解。该算法是又一种受自然界生物现象启示而产生的基于群体的协同搜索方法。